Bibliographic record
Abstract
We studied a system consisting of a proton, a muon, and an electron (a μpe system), the muon and the electron being in circular states. We demonstrated that in this case, the muonic motion can represent a rapid subsystem while the electronic motion can represent a slow subsystem – the result that might seem counterintuitive. We used a classical analytical description to find the energy terms for the quasi molecule where the muon rotates around the axis connecting the immobile proton and the immobile electron (i.e., dependence of the energy of the muon on the distance between the proton and electron). We found that there is a double-degenerate energy term. We demonstrated that it corresponds to stable motion. We also conducted an analytical relativistic treatment of the muonic motion and found that the relativistic corrections are relatively small. Then we unfroze the slow subsystem and analysed a slow revolution of the axis connecting the proton and electron. We derived the condition required for the validity of the separation into rapid and slow subsystems. Finally, we showed that the spectral lines, emitted by the muon in the quasi molecule, μpe, experience a red shift compared to the corresponding spectral lines that would have been emitted by the muon in a muonic hydrogen atom (in the μp-subsystem). The relative values of this red shift, which is a “molecular” effect, are significantly greater than the resolution of available spectrometers and thus can be observed. Observing this red shift should be one of the ways to detect the formation of such muonic–electronic negative hydrogen ions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".